aa r X i v : . [ a s t r o - ph ] F e b Astronomy&Astrophysicsmanuscript no. hm c (cid:13)
ESO 2018October 27, 2018
Uncertainties in (E)UV model atmosphere fluxes(Research Note)
T. Rauch
Institute for Astronomy and Astrophysics, Kepler Center for Astro and Particle Physics, Eberhard Karls University, Sand 1, D-72076T¨ubingen, Germany, e-mail: [email protected]
Received 21 January 2008 / Accepted 4 February 2008
ABSTRACT
Context.
During the comparison of synthetic spectra calculated with two NLTE model atmosphere codes, namely
TMAP and
TLUSTY ,we encounter systematic di ff erences in the EUV fluxes due to the treatment of level dissolution by pressure ionization. Aims.
In the case of Sirius B, we demonstrate an uncertainty in modeling the EUV flux reliably in order to challenge theoreticians toimprove the theory of level dissolution.
Methods.
We calculated synthetic spectra for hot, compact stars using state-of-the-art NLTE model-atmosphere techniques.
Results.
Systematic di ff erences may occur due to a code-specific cuto ff frequency of the H I Lyman bound-free opacity. This is thecase for
TMAP and
TLUSTY . Both codes predict the same flux level at wavelengths lower than about 1500 Å for stars with e ff ectivetemperatures ( T e ff ) below about 30 000 K only, if the same cuto ff frequency is chosen. Conclusions.
The theory of level dissolution in high-density plasmas, which is available for hydrogen only should be generalized toall species. Especially, the cuto ff frequencies for the bound-free opacities should be defined in order to make predictions of UV fluxesmore reliable. Key words.
Atomic data – Stars: atmospheres – Stars: individual: HZ 43, Sirius B – Stars: white dwarfs – Ultraviolet: stars – X-rays:stars
1. Introduction
NLTE model atmosphere codes for hot, compact stars havearrived at a high level of sophistication and are success-fully employed for spectral analyses, e.g. the T¨ubingenNLTE Model-Atmosphere Package
TMAP (Werner et al. 2003;Rauch & Deetjen 2003) in the case of LS V + ◦
21, the centralstar of Sh 2 −
216 (Rauch et al. 2007).In the case of high-gravity stars like LS V + ◦ g = . / sec ], T e ff =
95 000 K) or neutron stars (e.g.Suleimanov & Werner 2007), the consideration of the dissolu-tion of atomic levels by plasma perturbation (for details see, e.g.,Hummer & Mihalas 1988) is crucial for a reliable model atmo-sphere calculation (Hubeny et al. 1994).Beuermann et al. (2006, 2008) established the DA-typewhite dwarfs HZ 43 (log g = . T e ff =
51 111 K) and Sirius B(log g = . T e ff =
24 897 K) as soft X-ray standards. For a cross-calibration between the Chandra LETG + HRC-S, the EUVEspectrometer and the ROSAT PSPC, pure hydrogen
TMAP model atmospheres and synthetic spectra were used. In the caseof Sirius B with a higher surface gravity g (log g = . ffi cient(Fig. 1) and thus, it is more important to consider it properly.
2. Level dissolution
Recently, Jelle Kaastra (priv. comm.) has drawn our attentionto a deviation between
TMAP and
TLUSTY fluxes for Sirius B http: // astro.uni-tuebingen.de / ∼ rauch / TMAP / TMAP.html http: // nova.astro.umd.edu n = 14 5 2101 -8 -7 -6 -5 -4 -3 -2 -1 0 log m / g/cm o cc upa t i on p r obab ili t y Fig. 1.
Occupation probabilities of the lowest 14 H I levels con-sidered in our TMAP model atmosphere calculation for Sirius B.Note that the line formation takes place at log m ≈ − . − − . TMAP and
TLUSTY from time to time and found only negligible dif-ferences due to di ff erent numerical approaches and slightly dif-ferent constants. In an investigation of the flux discrepancy, weare now able to identify its reason. Both codes, TMAP as wellas
TLUSTY , follow a generalized form to consider the leveldissolution by Hubeny et al. (1994). A hitherto unsolved prob-lem, however, is a precise, generalized formulation of the ex-trapolation of the hydrogen Lyman bound-free opacity into apseudo-continuum below the unperturbed position of the absorp-
T. Rauch: Uncertainties in (E)UV model atmosphere fluxes (RN) o l og F λ / e r g / c m / s e c / c m Fig. 2.
Discrepancy between synthetic spectra for Sirius B calcu-lated by
TMAP (thick, long cuto ff , see text) and TLUSTY (thin,short cuto ff , Lanz priv. comm.) with the same parameters.tion threshold (cf. D¨appen et al. 1987). TMAP uses a heuristicapproach with ν thi = f · n − n i + · ν th , (1)where ν thi and ν th , are the extrapolated and unperturbed thresh-old frequencies, respectively, of level i and n i is its principalquantum number, i.e., n = f = λ th1 = . . Å, “short” cuto ff ), TMAP intro-duced f = . λ th1 = .
34 Å, “long” cut-o ff ) in order to achieve a smooth transition into the continuum(Fig. 3).
01 1500 1000 wavelength / A o - F λ / e r g / c m / s e c / c m Fig. 3.
Synthetic fluxes for Sirius B calculated from continuummodels (no line transitions considered for test reasons) with ashort (thin line) and a long cuto ff (thick). The dashed line showsa synthetic spectrum with neglection of the level dissolution.Note that the artificial absorption edge at the short cuto ff is hid-den in the strong L α absorption when those lines are considered(dotted). TLUSTY uses a di ff erent treatment of the continuum. Basedon the physical picture used to derive the pseudo-continuumformulation (cf. D¨appen et al. 1987), which is valid only nearthe ionization limit, an artificial “short” cuto ff of the bound-free opacity of the hydrogen Lyman-continuum at λ th1 =
925 Å(Lanz priv. comm.) may be chosen (
TMAP : λ th1 = .
34 Å).A test calculation has shown that the model atmosphere fluxesof
TMAP and
TLUSTY agree within 5 % if a long cuto ff is usedby TLUSTY , too (Lanz priv. comm., Fig. 4).
TMAP longTLUSTY shortTLUSTY long
123 400 350 wavelength / A o - F λ / e r g / c m / s e c / c m Fig. 4.
Comparison of
TMAP and
TLUSTY (dotted: long cuto ff ,dashed: short cuto ff ) fluxes in the vicinity of the largest deviation(Fig. 2).Test calculations of pure hydrogen models with TMAP via the WWW interface
TMAW at log g = . T e ff be-tween 10 000 and 50 000 K have shown that deviations be-tween short-cuto ff and long-cuto ff model fluxes are negligibleat T e ff > ∼
30 000 K due to the increasing degree of ionization. Thisexplains the good agreement of
TMAP and
TLUSTY fluxes incase of HZ 43.
3. Conclusions
Since no reliable theory is available, the choice of di ff erent cut-o ff frequencies of the H I Lyman bound-free opacity in the NLTEmodel-atmosphere codes
TMAP and
TLUSTY demonstrates thatthe estimate of the pseudo-continuum at longer wavelengths ispresently an uncertainty and definitely deserves further investi-gation. However, the necessity of a cuto ff in order to avoid anunrealistic opacity in the infrared is shown in Fig. 5.Moreover, a reliable theory for level dissolution by pressureionization is presently available only for H i . Since this is impor-tant for all other species as well, a generalized theory is highlydesirable. However, this is out of the scope of this work. Acknowledgements.
We are indebted to Jelle Kaastra, Thierry Lanz and IvanHubeny who originally found discrepancies in the X-ray / EUV calibrations ofBeuermann et al. (2006) between
TLUSTY and
TMAP model-atmosphere fluxes.They informed Klaus Beuermann about this issue ahead of their publication.This initiated a re-investigation of our flux calibration (Beuermann et al. 2006).We found two trivial errors (Beuermann et al. 2008) and a strong systematic dif-ference in the case of Sirius B. Special thanks go to Thierry Lanz who then cal-culated two
TLUSTY models with di ff erent cuto ff frequencies of the H I Lymanbound-free opacity and thus worked out the basic reason for the di ff erences be-tween TLUSTY and
TMAP .We thank Klaus Beuermann, Klaus Werner, and Valery Suleimanov forcomments and discussions.T.R. is supported by the
German Astrophysical Virtual Observatory projectof the German Federal Ministry of Education and Research (BMBF) under grant05 AC6VTB. http: // astro.uni-tuebingen.de / ∼ rauch / TMAW / TMAW.html. Rauch: Uncertainties in (E)UV model atmosphere fluxes (RN) s ho r t c u t o ff: . A o l ong c u t o ff: . A o unpe r t u r bed t h r e s ho l d o f l u x r a t i o Fig. 5.
Ratios of synthetic fluxes calculated by